Computing Node Polynomials

Counting algebraic curves with certain prescribed properties is an old problem going back more than 150 years. In this talk I will describe recent progress on the following question: How many algebraic plane curves with a given number of nodes and given degree pass through a sufficient number of generic points? This number turns out to be a polynomial (Fomin-Mikhalkin) if the degree is large. Using tropical geometry and ``floor diagrams" I will show you some new (node) polynomials and a few other results about them, and try to explain what all this has to do with string theory.